Questions tagged [formula-derivation]

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13
votes
3answers
6k views

Why is inductance (L) proportional with turns-square (N²)?

We start from the Maxwell's Equation $$ \mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0. $$ We take surface integration of ...
8
votes
2answers
25k views

Deriving the formula from 'scratch' for charging a capacitor

So the formula for charging a capacitor is: $$v_c(t) = V_s(1 - exp^{(-t/\tau)})$$ Where \$V_s\$ is the charge voltage and \$v_c(t)\$ the voltage over the capacitor. If I want to derive this formula ...
7
votes
2answers
2k views

Opamp Inverting Amplifier: The case of non-inverting input not being connected to ground

What is the relation between \$V_i\$ and \$V_o\$ when the non-inverting input is supplied with a non-zero voltage level? I have shared my formula derivation below, but I can't validate it since I can'...
4
votes
1answer
138 views

Equation to calculate voltage divider resistor value for an input of op-amp

I found this guide for a temperature sensing circuit design with NTC thermistor by Texas Instruments. According to my opinion, optimum R1 value is calculated so that the voltage divider can provide ...
4
votes
1answer
492 views

How to interpret the equation \$e=K_e.\omega_m\$ in a BLDC context?

After researching a while on the subject, I noticed that several sources state that the back-emf constant of a BLDC motor satisfies the following equation: $$ e = K_e.\omega_m $$ where: \$e\$ - ...
3
votes
3answers
5k views

independent control of frequency and duty cycle in 555 timer (formulas)

I want to control frequency and duty cycle of output pulse of 555 timer. I searched and find this schematic in a post in SOV but I don't know how calculate frequency and duty cycle in the circuit. ...
3
votes
2answers
19k views

When can I use the formula P=V^2/R?

I'm currently learning about the transportation of electrical energy through power lines. I now know that transporting current at a very high voltage cause minimal power loss compared to transporting ...
2
votes
4answers
10k views

How to Derive Capacitive- and Inductive Reactance Formula

I've been searching around the internet to find out how to derive the reactance formula for capacitors and inductors. But I couldn't really find anything, so I thought why not make a post about it. ...
2
votes
2answers
455 views

Is voltage divider formula stated wrong everywhere?

Sample voltage divider circuit: simulate this circuit – Schematic created using CircuitLab In this circuit, \$Vout\$ is, by Ohm's Law: $$ Vin * \frac{R2}{R1+R2} $$ But this circuit, by itself ...
2
votes
2answers
102 views

Calculating for current in a single transistor amplifier(almost common collector?)

I was given this circuit for a practice test during one of my classes, but we were never shown how to actually solve it. It's just been bugging me so I wanted to know how others solved for all the ...
2
votes
1answer
3k views

Solar Power Watts/Volts/Amps

I have a 12v battery that is rated at 220ah. I have solar panels rated at 500 watts total. I'm using a MPPT charge controller rated for 12/24 volts I only have a rudimentary understanding of ...
2
votes
1answer
50 views

How to deal with controling force by positioning oscillating magnet?

I am trying to code up a closed loop control system on force generated by the paring of strong rare earth magnets. I do not have much experience with PID logic but i have a weak grasp of the basics (...
2
votes
1answer
44 views

Trying to find value of two capacitors using resonant frequencies in three conditions, but wrong formula is derived

I was trying to find capacitance of two capacitors in the following way. Connect each capacitor individually to a same inductor and find resonant frequency in each case. Connect the same capacitors ...
2
votes
1answer
3k views

Current draw calculations for a brush-less motor are way off

I've been attempting to calculate how much current a BLDC will draw given a known propeller size, thrust, internal resistance, Kv rating, Supply Voltage(Vin) and idle current. My propeller parameters ...
2
votes
1answer
28 views

How to properly calculate current of a variable capacitor?

So the formula i(t)=CdV/dt works for a constant value of a capacitor, but in a variable capacitor, i found the next formula on another site i(t)=C(t)*dV(t)/dt + V(t)*dC(t)/dt Is this formula ...
2
votes
1answer
89 views

How do I derive \$(i_x)/(V_A-V_B)\$ in this circuit?

I have this circuit below: http://qph.is.quoracdn.net/main-qimg-a5380479d6b436dcfb9a36252ac3f1c1?convert_to_webp=true Can I make the small signal equivalent circuit as shown below and when doing the ...
2
votes
0answers
175 views

Current derivative in RLC circuit

How to find the current derivative(di/dt) at t = 0+ in the first loop?
1
vote
5answers
1k views

What is the origin of the capacitance formula?

Everyone knows capacitance is defined as C = Q/V, but why? Sure I understand the utility of it and its use, but can someone provide a motivation or historical context for this definition? I'm unable ...
1
vote
1answer
10k views

I/O Resistance of common source MOSFET with source degeneration

Common Source MOSFET with source degenerations looks like this I am a bit confused about different input and output resistance statements (provided by different sources). Some of them say that ...
1
vote
3answers
62k views

Relationship of Induction Motor Frequencies

I would like to know how the mechanical rotor frequency [Hz] can be obtained from the electrical stator frequency [Hz]? This is no homework! I have consulted several books as well as the web but could ...
1
vote
3answers
4k views

Common Source JFET small signal equivalent circuit

This circuit is equivalent to small-signal common source JFET amplifier: If you look at the input and output impedance you can see that Zin = R1 || R2 and Zout = rd || Rd || Rl. It can be seen from ...
1
vote
1answer
62 views

Derivation of energy in capacitor

While searching for something totally unrelated to this, I came a cross a website that derived it in this fashion: the instanteous power in a capacitor is given by $$p_c= v_c(t)\cdot i_c$$ since $$i_c(...
1
vote
2answers
7k views

How to derive the torque expression for a BLDC?

How can I derive the torque equation for a star-connected, brushless DC motor, given its back-emfs waveforms and currents? I'm currently reading the article A Park-like transform for the study and ...
1
vote
2answers
3k views

MOSFET finite output resistance in saturation mode

Since MOSFET has finite output resistance in saturation/active mode, the slope of unsignificanlty rising drain current is defined by Ua and slope parameter as lambda: This parameter (as I know) is ...
1
vote
2answers
195 views

Voltage divider equation tunnel diode - Art of Electronics

Early on in the book "The Art of Electronics" (p.15, 2nd edition) a voltage divider circuit is described: an input voltage \$V_{in}\$ over a tunnel diode \$D\$ and a resistor \$R\$, and an output ...
1
vote
4answers
761 views

Amplify 0 to 3.3V input to +/-3.3V

I'm working on modifying a board, while going through its schematic design I came across a section where a DAC output into the range of [0, +3.3V], which is then supposedly gained to +/-3.3V range, ...
1
vote
2answers
3k views

Help in plugging equation in arbritrary current source LTSpice

I cannot plug in the following equation and parameters in arbitrary current source. Any help would very appreciated. ltspice cannot read my parameters..
1
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3answers
3k views

Basic formula for calculating required cable area

Trying to do a spreadsheet to figure out how much cable of different dimensions I will need for a low voltage DC electrical system, but got stuck on the formula for converting current draw, distance ...
1
vote
1answer
130 views

Unknown Ψ variable in JFET's drain current equation

This question considers unipolar transistor, that is JFET. I really didn't find any other formula than this one which applies only for linear/ohmic/triode region of JFET U/I characteristic. What is ...
1
vote
2answers
480 views

Boost converter component selection

I want to design discrete boost converter with 5 volt input and 24 volt output with load current of 1 amp. How do I choose suitable input and output capacitor and inductor values; what formulas are ...
1
vote
1answer
231 views

math behind complex numbers C||RLC

I have a mathematical problem with the following formula. The goal is to transform this equation to have a seperated real and imaginary part. I have already done this with several other equasions, but ...
1
vote
1answer
242 views

How calculate inductor discharge time through LED?

UPDATE Overnight I realized I'd been sleeping as I read part of the textbook I've been using or at least didn't quite fully grasp the purpose of inductor volt-second balance. I added the results of ...
1
vote
1answer
4k views

How can the Nyquist theorem for the maximum bit-rate of a noiseless channel be derived?

I've been given the formula: $$ I = 2* H * log_2(L)$$ where: \$ I \$ = Maximum data rate in bits per second for a noiseless channel \$H\$ = Bandwidth that the channel will carry (that is, the range ...
1
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0answers
33 views

Is mmf the same as the magnetic force?

In the following system, I created the following equation in terms of what I assumed to be the force acting on the movable object with a mass M. The reluctance of the core is neglected, so the total ...
1
vote
1answer
198 views

Differential equation of a RRC circuit as Voltage output/voltage input?

So in this presentation i have got, there is a RRC circuit, and they get this differential equation, but there is no procedure explained how they have got it. This is basicially a series RRC circuit ...
1
vote
1answer
143 views

Deducing the value of a variable resistor in configurable voltage divider

Two variable resistors (RS & RE) and one static resistor (RC) are connected to a high impedance input analog input pin of a micro-controller. The static resistor is connected to ground and the two ...
1
vote
1answer
54 views

Calculate field strength for shielded isotropic transmitter

How to calculate the field strength of a shielded theoretical isotropic transmitter, if there is a hole in the shield for example. I am looking for a complex formula that also takes into account the ...
1
vote
0answers
630 views

JFET transconductance vs. MOSFET transconductance

JFET's n-channel highest transconductance (from datasheets) is marked as In theory, the same value is defined as that applies for n-channel JFET. I haven't found equation which defines MOSFET's ...
1
vote
0answers
51 views

Problem with complex numbers C||RLC [duplicate]

I would like to bring this formula in the form Re(D) + jIm(D): This is my current progress: My question is: How can I get rid of the imaginary part jωC2*R? When the denominator is completely real ...
1
vote
1answer
50 views

Derivatives in time and phasor domains do not match

Given that voltage can be represented in the time domain as the following: $$V(t) = \vec{\mathbf{|V|}}\cos{(\omega t + \phi_V)}$$ It can be shown that in the phasor domain, this is the equivalent ...
0
votes
3answers
359 views

Why do most textbooks use the inverse formula 1/rtotal for parallel resistance?

I was calculating the parallel resistance for a circuit, but just couldn't get the correct answer despite several attempts. I felt incredibly dumb when I watched a video on how to calculate parallel ...
0
votes
3answers
164 views

Is this a proper way to find the derivate of a 12-bit ADC?

I'm seeking a solution to find the derivative of an 12-bit ADC. It's for STM32 but let's say it's for likely for an arbitrary micro controller. ...
0
votes
2answers
415 views

MOSFET Biasing Problems

I am interested in finding Vgs for E-MOSFET for desired Id or/and Vds. Referring to those equations of drain current in saturation region, value of conduction parameter "K" would be nice to have but ...
0
votes
3answers
1k views

How to differ output & input resistance of small-signal model BJT?

I understand how input and output resistance of small-signal model for bipolar transistor is defined and how draw one. What I don't understand quite yet is how actually input and output resistance of ...
0
votes
1answer
133 views

Inductance of Shielded Helical Resonators

I found an equation in a thesis which calculates the inductance for a helical coil inside of a cylindrical shield: $$L = (\pi N d_{coil})^{2}\frac{1}{l_{coil} +0.45 d_{coil}}\left(1 -\frac{d_{coil}^{...
0
votes
1answer
519 views

How do I calculate, or measure, all values in a simple A.C. circuit?

I'm trying to figure out how all the formulae fit together regarding A.C. currents. Given this circuit and equations: I figured out the following: ...
0
votes
1answer
60 views

Deriving Wheatstone bridge equation

I have the following circuit: Here I have obtained the equation of Ud = U * ((deltaR / R)/(4+2(deltaR/R))). But I'm stuck on the part on how to derive that formula. Any help or guidance is ...
0
votes
1answer
177 views

Confusion with derivation of average power formula [closed]

I know that average power is equal to \$VmIm/2 * PF\$. I can show that this is equivalent to \$(1/2)Re(VI^*)\$ by writing VI* in magnitude phase form. However, I also know that complex power \$S = ...
0
votes
2answers
2k views

Common drain JFET output resistance “problem”

The output resistance of small signal model for common drain JFET amplifier equals $$ \frac{1}{g_\text{m}} || R_{\text{ds(on)}} \parallel R_\text{S} $$ and since $$ R_{\text{ds(on)}} =\frac{1}{g_\text{...
0
votes
1answer
4k views

Real output resistance of MOSFET

This question is related to MOSFET. NMOSFET's resistance was till now defined in many different ways, for example as: or which value varies from 1-50k Ohm. And there is also drain-source on-state ...